Stochastic modelling of crack propagation in materials with random properties using isometric mapping for dimensionality reduction of nonlinear data sets

Fractures tend to propagate along the least resistance paths, and homogeneous-based models may not be able to reliably predict the true crack paths, as they are not capable of capturing nonlinearities and local damage induced by local inhomogeneity. This paper presents a stochastic numerical modelling framework for simulating fracturing in natural heterogeneous materials. Fracture propagation is modelled using Francfort and Marigo's variational theory, and randomness in the material properties is introduced by random field principle. A computational strategy on the basis of nonlinear dimensionality reduction framework is developed that maps domain of spatially variable properties of the materials to a low-dimensional space. This strategy allows us to predict the most probable fracture patterns leading to failure by an optimisation algorithm. The reliability and performance of the developed methodology are examined through simulation of experimental case studies and comparison of predictions with measured data.

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